Place garlic and chilies in a mortar and pound into a paste. Add brown sugar and Thai long beans, pound again until the sugar is dissolved. Add tomatoes and gently pound. → You can work in batches if your mortar is too small.
Peel, then cut green papaya and carrot in julienne strips using a julienne peeler.
Place green papaya and carrot along with the pounded ingredients, lime juice, soy sauce, and half of the crushed peanuts in a large bowl. Toss to combine. → What I learned in Thailand is to pound all ingredients with the pestle in one hand while tossing the ingredients with a spoon in the other hand for about one minute.
Serve in a large bowl and sprinkle with the remaining peanuts.
Notes
Thai Long Beans (Thai Green Beans) can be found at the Asian Market. Can be omitted or substituted with blanched green beans.
Green Papaya is available in Asian Markets. Alternatively, substitute with 1-2 English cucumbers. The taste won't be the same, but it's a great way to not miss out on this delicious Thai salad, even if you can't get your hands on green papaya.
Leftovers can be stored in an airtight container in the refrigerator for up to 1 day.